Graphite Whiskers, Cones, and Polyhedral Crystals169Furthermore, out-of-plane bending of the hexagonal carbon rings along the polygonal edges brings new pairs of atoms closer than the second-neighbor distance in graphite. All this leads to the modification of the electronic band structure, and as a consequence, the semiconducting band gap of the (10, 0) polygonal tube is almost completely closed (Figure 4.21b). The ab initio calculations134 confirm these tight-binding results and predict a gap of 0.08 eV for the pentagonal cross section. Electronic behavior of metallic armchair nanotubes is not so strongly altered with polygonization because the 蟽 *撓�* hybridization is not possible in the case of armchair configurations. Theoretical studies also suggest that the perturbation of electronic properties of carbon nanotubes will be different for various degrees of polygonization (i.e., various numbers of facets).134 An example is given for a (12, 0) nanotube. Zigzag (12, 0) nanotube of circular cross section is metallic. When different polygonal cross sections (triangle, square, and hexagon) are considered, the results indicate that all kinds of electronic properties arise (Figure 4.22). The first two cases are metallic, while the third is a 0.5 eV band gap semiconductor. It is important to remember here that these calculations are given for a carbon nanotube comprised of a single shell. 4.3.3.2 Raman Spectra Vibrational properties of GPCs have been studied by means of Raman spectroscopy,42,102,115 and it has been confirmed that they are highly graphitized structures with the distinct disorder-induced (D) band and the strong graphitic (G) band of about the same full-width at half-maximum (FWHM = 14 cm 1) as in crystals of natural graphite.136 The selective micro-Raman spectra from the crystal side face and tip are shown in Figure 4.23. Spectra from the crystal faces correspond to perfect graphite with a narrow G band at 1580 cm �. In addition to 1580 cm 1 peak, the spectra from the tips feature a weak D band at 1352 cm�, and an unusually strong 2-D (2706 cm 1) overtone that exceeds the intensity of the G band. A similar effect was observed on graphite scrolls (Figure 4.15). Raman spectra of GPCs contain two additional bands in the second-order frequency range at ca. 1895 and 2045 cm 1 (Figure 4.23). A number of weak low-frequency bands including a doublet at 184/192 cm 1 have been observed in some samples.42 These low-frequency bands, typical for single-wall nanotubes,137 may come from the innermost carbon nanotube shells protruding(a)(12,0)3 2.0 1.5 1.0 0.5 0.0 �.5 �.0 �.5 �.0 �.5 螕 X EF(b) (12,0)4 2.0 1.5 1.0 0.5 0.0 �.5 �.0 �.5 �.0 �.5 螕 X EF(c) (12,0)6 2.0 1.5 1.0 0.5 0.0 �.5 �.0 �.5 �.0 �.5 螕 X EF(d) (12,0) 2.0 1.5 1.0 0.5 0.0 �.5 �.0 �.5 �.0 �.5 螕 X EFFIGURE 4.22 Tight-binding band structures of the metallic (12, 0) nanotube, illustrating the effect of the degree of polygonization of the cross section on electronic behavior. Given here are examples of (a) the triangle (12, 0)3, (b) square (12, 0)4, and (c) hexagonal (12, 0)6 geometries that are compared to the pure cylinder case tube (d).134 2006 by Taylor and Francis Group, LLCEnergy (eV)
